New Method of Quickly Mapping Phase Diagrams of Polymer Solutions over a Wide Concentration Range

Many industrial applications require a quick method to determine the chain length-dependent phase diagram of a given polymer solution, such as converting a solution polymerization into a precipitation polymerization, to greatly save the cost. However, it is rather difficult and time-consuming to precisely map phase diagrams of polymer solutions with different chain lengths, so that good phase diagrams are scarcely documented in the literature. The difficulties come from two facts: (1) one has to prepare polymer solutions with different concentrations and chain lengths first, and then (2) measure the temperature dependent on each solution carefully, normally taking months if not years. In this study, the chain length and temperature-dependent scaling laws for linear polymer phase diagrams were established as ${\Phi }_l={\Phi }_C-{{\Phi }_0}^{*}{N}^{-0.22}{\left(\frac{T_C-T}{T_C}\right)}^{0.326}+{{\Phi }_1}^{*}{N}^{0.014}{\left(\frac{T_C-T}{T_C}\right)}^{0.827}$ and ${\Phi }_h={\Phi }_C+{{\Phi }_0}^{*}{N}^{-0.22}{\left(\frac{T_C-T}{T_C}\right)}^{0.326}+{{\Phi }_2}^{*}{N}^{0.014}{\left(\frac{T_C-T}{T_C}\right)}^{0.827}$for concentrations (Φ_l and Φ_h) lower and higher than the critical concentration (Φ_C), where T_C is the critical temperature; and Φ₀, Φ₁, and Φ₂ are the chain-length independent parameters. Armed with these scaling laws, we have developed a quick optical method to map the coexistence curve of the phase diagram of each kind of polymer solution by measuring the phase transition temperatures of five or more polymer solutions with a given chain length but different concentrations to determine the five parameters Φ_C, T_C, Φ₀, Φ₁, and Φ₂.